Ontology-based data access (OBDA) is a technology where heterogeneous, distributed data is accessed through queries over an ontology which provides domain-specific knowledge. The ontology is connected to the stored data using mappings, which are commonly interpreted as first-order implications from the source language to the ontology language. I propose to generalize OBDA mappings using defaults from default logic. The resulting mapping language is much more expressive than standard mapping languages, while retaining all the desired properties related to query answering in OBDA systems. This would allow the statement of epistemic queries and greatly reduce maintenance cost and potential for error in lack of knowledge and exception handling.